The meshing consists of dividing the domain into a set of geometric elements, also called cells. Each cell and the set of cells in its entirety must meet predefined validity conditions, for example pertaining to the geometric shape of the cells (square, triangle, tetrahedron, hexahedron, cube, etc.) or apical angle values (compliance with minimum/maximum angle values). These predefined conditions depend in large part on the application for which the mesh is intended.
A number of methods exist for generating a mesh of a domain.
Known in particular are methods based on the optimization of an objective function depending on the coordinates at the apices of the cells. Such methods are sometimes called “variational methods.” To define the objective function, these methods use Centroidal Voronoi Tessellation (CVT) and Optimal Delaunay Triangulation (ODT).
Variational methods make it possible to effectively and robustly generate isotropic meshes using what are called simplicial complexes. These methods are particularly effective when an anisotropic mesh is to be generated from triangular elements (meshing a surface) or tetrahedral elements (meshing a volume).
For certain applications, however, it is necessary, or at least preferable, to use meshes generated from hexahedral elements (volume), or quadrilateral-shaped elements (surface). This is for example the case for certain simulations using finite elements or numerical analyses, in particular in the field of fluid dynamics, the design of reservoirs for oil exploration, or mechanics in the plastic or highly elastic domains. In this type of application, using a executable mesh makes it possible to obtain both a more reliable simulation and a reduced number of elements to which the simulation pertains.
“Hexahedral mesh,” or more accurately “dominant executable mesh,” refers to a mesh primarily having hexahedral elements. A dominant hexahedral mesh may also comprise elements of different shapes, in particular tetrahedral elements, provided that the hexahedral elements are larger in number and/or volume than the elements of a different shape.
Furthermore, certain applications may require the generation of an anisotropic mesh, i.e. a mesh having elements that differ from one another in terms of size and/or orientation, in predefined zones of the domain.
To date, no fully satisfactory method exists for generating meshes from hexahedral or quadrilateral elements. The current methods require a manual intervention during the meshing operation. Furthermore, these methods have a significant calculation time, much higher than the traditional variational methods (by several orders of magnitude), which makes them nearly unusable in practice. Furthermore, they do not make it possible to define an anisotropy in the meshing.
The invention aims to improve the situation.